By Anthony E. Armenàkas
CARTESIAN TENSORS Vectors Dyads Definition and ideas of Operation of Tensors of the second one Rank Transformation of the Cartesian parts of a Tensor of the second one Rank upon Rotation of the approach of Axes to Which they're Referred Definition of a Tensor of the second one Rank at the foundation of the legislation of Transformation of Its elements Symmetric Tensors of the second one Rank Invariants of the Cartesian parts of a Symmetric Tensor of the second one Rank desk bound Values of a functionality topic to a Constraining Relation desk bound Values of the Diagonal elements of a Symmetric Tensor of the Second. Read more...
summary: CARTESIAN TENSORS Vectors Dyads Definition and ideas of Operation of Tensors of the second one Rank Transformation of the Cartesian elements of a Tensor of the second one Rank upon Rotation of the method of Axes to Which they're Referred Definition of a Tensor of the second one Rank at the foundation of the legislation of Transformation of Its parts Symmetric Tensors of the second one Rank Invariants of the Cartesian elements of a Symmetric Tensor of the second one Rank desk bound Values of a functionality topic to a Constraining Relation desk bound Values of the Diagonal parts of a Symmetric Tensor of the second one
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Additional resources for Advanced Mechanics of Materials and Applied Elasticity
10b was constructed from the specified values of the components A11, A22, A12 of a quasi plane symmetric tensor of the second rank referred to the set of axes x1, x2. Consider another set of axes xN, 1 xN2 in the x 1 x 2 plane which, as shown in Fig. 10a, is obtained by rotating the x1, x2 axes counterclockwise by the angle about the x3 axis. We shall determine the components AN11, AN12 of the tensor geometrically, with the aid of Mohr's circle. We designate the point on Mohr's circle whose coordinates are A11, A12 by X1 and the point whose coordinates are AN11, AN12 by XN1 and we suppose that XN1 is located clockwise from point X1.
C) What is the equation of the plane x1 ! x2 + 2x3 = 1 in the system of axes xN. i Ans. 7. 4). Ans. 315) (b) What are the components of a tensor A = ! 2i1i2 + i2i2 !
A) Determine the unit vector acting from point P1 to point P2. (b) Determine the angles pP1OP2 and pOP1P2, where O is the origin of the axes of reference. (c) Determine the unit vector normal to the plane specified by the points O, P1, P2. (d) Compute the volume of the parallelepiped whose edges are OP1, OP2 and OP3. Ans. 27o (c) (d) 8 m3 2. Consider the rectangular system of axes xNi (i = 1, 2, 3) specified with respect to the rectangular system of axes xj by the transformation matrix 45 Problems The cartesian components of a vector referred to the rectangular system of axes xj are a = 4i1 + 3i2.
Advanced Mechanics of Materials and Applied Elasticity by Anthony E. Armenàkas